A Multiscale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering

TLDR

Voronoi meshes are unstructured grids that allow variable horizontal resolution. The authors develop MPAS‑A, a fully compressible nonhydrostatic model that uses these variable‑resolution Voronoi meshes to enable embedded high‑resolution regions for regional NWP and climate applications. MPAS‑A discretizes the equations on centroidal Voronoi meshes with a C‑grid staggering of prognostic variables, employs split‑explicit time integration, and can be applied on the globe, limited areas, or Cartesian planes. Tests show the solver is as accurate as existing nonhydrostatic solvers for small‑scale flows and comparable to global icosahedral models for large‑scale flows, while preliminary full‑physics forecasts demonstrate robustness and well‑resolved variable‑resolution solutions with no problems at mesh‑transition zones.

Abstract

Abstract The formulation of a fully compressible nonhydrostatic atmospheric model called the Model for Prediction Across Scales–Atmosphere (MPAS-A) is described. The solver is discretized using centroidal Voronoi meshes and a C-grid staggering of the prognostic variables, and it incorporates a split-explicit time-integration technique used in many existing nonhydrostatic meso- and cloud-scale models. MPAS can be applied to the globe, over limited areas of the globe, and on Cartesian planes. The Voronoi meshes are unstructured grids that permit variable horizontal resolution. These meshes allow for applications beyond uniform-resolution NWP and climate prediction, in particular allowing embedded high-resolution regions to be used for regional NWP and regional climate applications. The rationales for aspects of this formulation are discussed, and results from tests for nonhydrostatic flows on Cartesian planes and for large-scale flow on the sphere are presented. The results indicate that the solver is as accurate as existing nonhydrostatic solvers for nonhydrostatic-scale flows, and has accuracy comparable to existing global models using icosahedral (hexagonal) meshes for large-scale flows in idealized tests. Preliminary full-physics forecast results indicate that the solver formulation is robust and that the variable-resolution-mesh solutions are well resolved and exhibit no obvious problems in the mesh-transition zones.